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Simplifying 25x2 + -40x + 1 = 0 Reorder the terms: 1 + -40x + 25x2 = 0 Solving 1 + -40x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.04 + -1.6x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + -1.6x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + -1.6x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + -1.6x + x2 = 0 + -0.04 -1.6x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 -1.6x + x2 = -0.04 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = -0.04 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.04 + 0.64 Combine like terms: -0.04 + 0.64 = 0.6 0.64 + -1.6x + x2 = 0.6 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (x + -0.8) equal to 0.774596669 and -0.774596669.Subproblem 1
x + -0.8 = 0.774596669 Simplifying x + -0.8 = 0.774596669 Reorder the terms: -0.8 + x = 0.774596669 Solving -0.8 + x = 0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.774596669 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.774596669 + 0.8 x = 0.774596669 + 0.8 Combine like terms: 0.774596669 + 0.8 = 1.574596669 x = 1.574596669 Simplifying x = 1.574596669Subproblem 2
x + -0.8 = -0.774596669 Simplifying x + -0.8 = -0.774596669 Reorder the terms: -0.8 + x = -0.774596669 Solving -0.8 + x = -0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -0.774596669 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.774596669 + 0.8 x = -0.774596669 + 0.8 Combine like terms: -0.774596669 + 0.8 = 0.025403331 x = 0.025403331 Simplifying x = 0.025403331Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.574596669, 0.025403331}
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